I don't think they will just write to you with a settlement offer. My hunch is they will write and say 'you were caught - we believe this has happened on other occasions, we are minded to take you to court - what is your side of the story?' type thing.
Then you will have to reply along lines you state and if lucky you will get offered a settlement.
I would think the problem comes when if that settlement is based on higher evaded fares than you have done, the extent to which they are prepared to enter into a debate about that (using the excellent advice from
@Fawkes Cat ) rather than just withdraw the settlement offer and 'see you in court' - where you will be guilty of at least one occasion that is an offence at least - so then you get the criminal record that you have stated is something you seriously wish to avoid - this the only way to avoid that is thus to pay the settlement offer - even if it is inflated (should just be offered of course).
Although the question gets raised we do not seem to see many examples of people 'negotiating down' the settlements based on debates about the number of genuine fare dodges made to a location that they may also travel to. Whether this is because people don't report back or they just get nowhere I can not say.
I doubt they are going to go trawling through loads of old CCTV - it's more a case of 'give us £x00 to settle or we will take you to court'. If you don't want to go to court there is not much to do apart from pay the settlement asked it seems to me.
But for certain, start getting your evidence that supports legitimate visits to Hatfield (or other places) since if you wish to reply to the railway and admit the genuine offences (
doing this may not be wise however) it would then allow you to list the genuine visits and back that up with evidence to support those occasions in the hope that the railway will accept and believe them.
No idea on that one - I guess that might depend on if they look to them like they may also be 'short fares' and thus they have a suspicion to put to you. So it probably depends on the fares concerned. EG if you bought a Welwyn to Peterborough ticket I can't see them accusing you of actually going to York say, without any evidence to support that.
